DRAFT TRANSFER GOALS, UNDERSTANDINGS, AND ESSENTIAL QUESTIONS FOR
MATHEMATICAL PRACTICES
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Transfer Goals:
Based on an understanding of any problem, initiate a plan, execute it and evaluate the reasonableness of the
solution.
Examine alternate methods to accurately and efficiently solve problems.
Use appropriate tools strategically to deepen understanding of mathematical concepts.
Articulate how mathematical concepts relate to one another in the context of a problem or in the theoretical
sense.
Mathematical
Practices
Understandings
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1. Make sense of
problems and
persevere in
solving them.
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2. Reason
abstractly and
quantitatively.
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3. Construct
viable arguments
and critique the
reasoning of
others.
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Effective problem solvers work to
understand the problem before trying to
solve it.
Effective problem solvers identify relevant
information.
Effective problem solvers identify and
apply an appropriate model, tool, or
strategy.
Effective problem solvers try multiple
strategies when struggling.
Every problem is a member of a category
of problems that has a similar structure and
set of characteristics.
Placing a problem in a category gives you a
familiar approach to solving it.
Mathematicians use diagrams, symbols, and
terms to describe problems or situations.
Essential Questions
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Effective arguments are based on logical
mathematical thinking.
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Evaluating arguments creates clarity about a
problem, its model, and the viability of a
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solution.
What is a reasonable estimate?
What do I picture/visualize when I look
at this problem?
What is important here? What is not
important?
What strategies/approaches are best for
this problem?
What do I do when I get stuck?
Is my answer correct? OR Does my
solution make sense?
If not, how can I fix it? How can I
avoid this error the next time?
What type(s) of problem is this?
What characteristics/attributes define
this type of problem?
What information is needed and how
do I use it to solve a problem?
How could this strategy be used to
solve similar problems?
What does the solution represent?
Does the argument/thought
process/logic make sense?
What questions can I ask to help clarify
the argument/thought process/logic?
If an argument/thought process/logic
doesn’t make sense, what
revisions/changes to the plan or
argument are necessary?
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4. Model with
mathematics.
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5. Use
appropriate tools
strategically.
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Every problem belongs to a category of
problems that has a similar structure and set 
of characteristics; which means it can be
solved using a similar model.
Models can distort or reveal patterns;
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therefore it is essential to recognize the
appropriate representation.
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Is this problem similar to a problem I
have solved before?
What values, numbers, quantities,
and/or symbols can be used to solve a
problem?
Which model best represents this
problem?
How do I use the model to solve other
problems?
The choice of a mathematical tool depends
upon the information you have and the
information you want.
The accuracy of a solution depends upon
the proper selection and effective use of a
mathematical tool.
What tool(s) is appropriate for use with
this model?
How do I use tools to solve problems?
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6. Attend to
precision.
Attention to detail, such as specifying units
of measure and labeling, leads to clarity in
expressing mathematical information.
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7. Look for and
make use of
structure.
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Patterns and structures are characterized by
consistent relationships.
Recognition of patterns and structures
fosters efficiency in solving problems.
Mastery of basic facts and rules maximizes
conceptual and procedural fluency.
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8. Look for and
express regularity
in repeated
reasoning.
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Apply patterns and structures effectively to
efficiently solve problems.
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Did I use clear language (symbols,
labels, terms, units of measure and
significant digits) to explain my
reasoning to others?
How precise do my quantities need to
be for my calculations to be accurate?
Does my solution make sense?
What is the pattern/structure in this
problem?
How does understanding the
pattern/structure help me solve the
problem?
How do values and/or concrete models
relate to each other?
How does being fluent with basic facts
and rules help me solve a complex
problem?
How can the repeated application of a
process/structure help me solve
problems more efficiently?
Is this problem similar to a problem
that I solved before?
How does understanding the
pattern/structure help me solve the
problem?